F-1(x)=-2/x-2

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Solution for F-1(x)=-2/x-2 equation:



-1(F)=-2/F-2
We move all terms to the left:
-1(F)-(-2/F-2)=0
Domain of the equation: F-2)!=0
F∈R
We get rid of parentheses
-1F+2/F+2=0
We multiply all the terms by the denominator
-1F*F+2*F+2=0
We add all the numbers together, and all the variables
2F-1F*F+2=0
Wy multiply elements
-1F^2+2F+2=0
a = -1; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-1)·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*-1}=\frac{-2-2\sqrt{3}}{-2} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-1}=\frac{-2+2\sqrt{3}}{-2} $

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